Explicație pas cu pas:
x○y = 5xy - 5x - 5y + 6 = 5(x - 1)(y - 1) + 1
x○x = 5(x - 1)(x - 1) + 1 = 5(x - 1)² + 1
legea ○ este asociativă =>
x○x○x = (x○x)○x = 5[5(x - 1)² + 1 - 1](x - 1) + 1
= 25(x - 1)²(x - 1) + 1 = 25(x - 1)³ + 1
x○x○x = x
25(x - 1)³ + 1 = x
25(x - 1)³ - (x - 1) = 0
(x - 1)(5²(x - 1)² - 1) = 0
(x - 1)(5x - 5 - 1)(5x - 5 + 1) = 0
(x - 1)(5x - 6)(5x - 4) = 0
=>
x₁ = 1
x₂ = 6/5
x₃ = 4/5
